Generation of solitons and breathers in the extended Korteweg–de Vries equation with positive cubic nonlinearity

DOI10.1063/1.3279480zbMath1311.35218OpenAlexW2073947354WikidataQ43108583 ScholiaQ43108583MaRDI QIDQ5250396

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Publication date: 19 May 2015

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.3279480

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Scattering theory for PDEs (35P25) Solutions to PDEs in closed form (35C05) Soliton solutions (35C08)

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Cites Work

• Interactions of breathers and solitons in the extended Korteweg-de Vries equation
• On interfacial waves over random topography
• Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity
• Variationally obtained approximate eigenvalues of the Zakharov-Shabat scattering problem for real potentials.
• Structural transformation of eigenvalues for a perturbed algebraic soliton potential.
• The Modified Korteweg-de Vries Equation
• The soliton number of optical soliton bound states for two special families of input pulses
• Short‐Lived Large‐Amplitude Pulses in the Nonlinear Long‐Wave Model Described by the Modified Korteweg–De Vries Equation
• Internal solitons in laboratory experiments: Comparison with theoretical models
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• On the generation of solitons and breathers in the modified Korteweg–de Vries equation
• LONG NONLINEAR INTERNAL WAVES
• Short-lived two-soliton bound states in weakly perturbed nonlinear Schrödinger equation
• Generation of large-amplitude solitons in the extended Korteweg–de Vries equation
• Wave group dynamics in weakly nonlinear long-wave models

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